Question

How do you solve $-2x+3y=15$ and $-6x+6y=18$ using substitution ?

Answer 1

Hint: Now to solve the equation we will first simplify the equation $-6x+6y=18$ and simplify it to write the equation as $y=ax+b$ . Hence Now we have the value of y in terms of x. We will substitute the value of y in the equation $-2x+3y=15$ and solve to find x. Now we will use this value of x in any equation to find the value of y.

Complete step by step solution:
Now consider the two given equations $-2x+3y=15$ and $-6x+6y=18$
We want to find the solution of the given equation. Hence we want to find the values of x and y which satisfy both the equations. To find the solution of the equation we will use a method of substitution.
Now consider the equation $-6x+6y=18$ .
Now we will use the above equation to find the value of y in terms of x.
To do so first we will simplify the equation by dividing the whole equation by 6. Hence we get,
$\Rightarrow -x+y=3$
Now we will transpose x to RHS. Hence we get,
$\Rightarrow y=3+x$
Now we have the value of y in terms of x.
Hence we will substitute the value of y in the equation $-2x+3y=15$.
$\Rightarrow -2x+3\left( 3+x \right)=15$
Now on simplifying the above equation we get,
$\begin{align}
  & \Rightarrow -2x+9+3x=15 \\
 & \Rightarrow x+9=15 \\
 & \Rightarrow x=15-9 \\
 & \Rightarrow x=6 \\
\end{align}$
Hence the value of x is 6.
Now we will substitute the value of x in the equation $y=3+x$ hence we get y = 9.
Hence the solution of the given equations is x = 6 and y = 9.

Note: Now note that here we have two equations out of which we have used one for writing y in terms of x. Now while substituting remember to substitute the value of y in the other equation which hasn’t been used yet. Also note that we can also write x in terms of y to solve the equation.